Finite Group Databasebeta

← C11×#2032 #13064870

Subgroups — C11×#2032 #13064870

Order 1408.

278 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 80 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#543C211yesmaximal, characteristic, complemented
2C2×C11×#99C213yesmaximal
3C11×#342C213yesmaximal, complemented
4C22×D4×C11C2211yescharacteristic
5C11×C22⋊Q8—26no—
6C2×C11×C22⋊C4C2213yes—
7C2×C11×C22⋊C4C2213yes—
8C11×#99—26no—
9C24×C11Q811yescharacteristic, complemented
10C24×C11C2311yescharacteristic
11C2×Q8×C11—22no—
12C2×D4×C11—23no—
13C2×D4×C11—23no—
14C22×C4×C11—23no—
15C22×C4×C11—23no—
16C22×C4×C11Q811yescharacteristic, complemented
17C11×C4⋊C4—26no—
18C11×C22⋊C4—23no—
19C11×C22⋊C4—23no—
20C11×C22⋊C4—23no—
21C11×C22⋊C4D416yes—
22#2032C1111yesmaximal, characteristic, direct product factor, Sylow
23C23×C11—23no—
24C23×C11—81no—
25C23×C11—81no—
26C23×C11C2×D413yes—
27C23×C11C2×Q811yescharacteristic
28C23×C11#4113yes—
29Q8×C11—82no—
30D4×C11—41no—
31D4×C11—43no—
32C2×C4×C11—26no—
33C2×C4×C11—23no—
34C2×C4×C11—43no—
35C2×C4×C11—83no—
36C2×C4×C11—83no—
37#543C2×C1111yescharacteristic, complemented
38C2×#99C2×C1113yes—
39#342C2×C1113yescomplemented
40C22×C11—43no—
41C22×C11—43no—
42C22×C11—41no—
43C22×C11—41no—
44C22×C11—83no—
45C22×C11#12011yescharacteristic
46C22×C11C22⋊Q813yes—
47C22×C11#12413yes—
48C4×C11—46no—
49C4×C11—41no—
50C4×C11—83no—
51C22×D4C22×C1111yescharacteristic
52C22⋊Q8—26no—
53C2×C22⋊C4C22×C1113yes—
54C2×C22⋊C4C22×C1113yes—
55#99—26no—
56C2×C11—21no—
57C2×C11—23no—
58C2×C11—23no—
59C2×C11—81no—
60C2×C11#39311yescharacteristic
61C24Q8×C1111yescharacteristic, complemented
62C24C23×C1111yescharacteristic
63C2×Q8—22no—
64C2×D4—23no—
65C2×D4—23no—
66C22×C4—23no—
67C22×C4—23no—
68C22×C4Q8×C1111yescharacteristic, complemented
69C4⋊C4—26no—
70C22⋊C4—23no—
71C22⋊C4—23no—
72C22⋊C4—23no—
73C22⋊C4D4×C1116yes—
74C11#203211yescharacteristic, direct product factor, Sylow
75C23—23no—
76C23—81no—
77C23—81no—
78C23C2×D4×C1113yes—
79C23C2×Q8×C1111yescharacteristic
80C23C11×#4113yes—
81Q8—82no—
82D4—41no—
83D4—43no—
84C2×C4—26no—
85C2×C4—23no—
86C2×C4—43no—
87C2×C4—83no—
88C2×C4—83no—
89C22—43no—
90C22—43no—
91C22—41no—
92C22—41no—
93C22—83no—
94C22C11×#12011yescharacteristic
95C22C11×C22⋊Q813yes—
96C22C11×#12413yes—
97C4—46no—
98C4—41no—
99C4—83no—
100C2—21no—
101C2—23no—
102C2—23no—
103C2—81no—
104C2C11×#39311yescharacteristic
subgroupG/H
center, socleC2×C11#393
commutator, Frattini, cosocleC24C23×C11
prime radicalC22×D4×C11C22
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C2×C11 ◁ C24×C11 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C11×#543C2semidirect
3. C11×#342C2semidirect
9. C24×C11Q8semidirect
16. C22×C4×C11Q8semidirect
22. #2032C11direct (N × H)
37. #543C2×C11semidirect
39. #342C2×C11semidirect
61. C24Q8×C11semidirect
68. C22×C4Q8×C11semidirect
74. C11#2032direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C11×#5432
C2×C11×#992
C11×#3422
#203211